A tight single-change covering design with block size 6

Richard Bean

combinatorics

A tight single-change covering design with block size 6

arXiv:2607.10978

summary

The paper constructs a tight single‑change covering design with parameters v=26 and block size k=6, resolving an open problem about the existence of such designs with block size greater than 5, and details the SAT‑based search that discovered it.

Abstract

We give a tight single-change covering design with $v = 26$ and $k = 6$ . This answers Problem 1 of the Nineteenth British Combinatorial Conference, which asked whether such a design exists with block size greater than $5$ . We also describe the satisfiability search that found the design, including negative search results at the smallest admissible order $v = 21$ .

9 pages

Topics & keywords

#covering design #single-change design #block design #satisfiability search #combinatorial optimizationtight covering designblock size 6SAT solverdesign existence problemBritish Combinatorial Conference